Schematizing the paradoxes---and showing that hypodoxes are paradoxical

[Marco P.]

Bom dia,

Talvez seja de interesse da lista, achei curioso o tema da palestra.

Atenciosamente,

Marco 

 

July 1st, 4:30 pm - 6 pm
Speaker: Alexandre Billon (IJN & Lille)
Commentator: Ekaterina Kubyshkina (Université Paris 1, IHPST)
Title: Schematizing the paradoxes---and showing that hypodoxes are paradoxical
Abstract:
There is a long tradition, going back at least to Richard (1905), Poincaré (1906) and Russell (1906), of blaming circular definitions for the so-called ‘paradoxes of self- reference’. In this paper, I draw on this old idea to put forward a paradox schema that fits many of these paradoxes, including Russell’s paradox, the Liar, Berry’s paradox and Curry’s paradox. According to this schema, which I call the Elusiveness Schema, all these paradoxes hinge on the definition of an object which is at least implicitly circular. In each case, we have good reason to believe both that this definition succeeds in picking its definiendum, and that it fails because of vicious circularity. Hence the paradox.
This paradox schema has a few interesting features which make it fruitful. It applies, in particular, similarly to the classical paradoxes and to what is often called ‘the duals’ of these paradoxes (the set whose members are a member of themselves, the Truth- Teller sentence Tt =‘Tt is true’, etc.). While these duals are not usually considered paradoxical—it is sometimes said that they are merely ‘pathological’ or that they are `hypodoxes'—the Elusiveness Schema shows that they are in fact genuinely paradoxical. This has consequences both for the classification of the paradoxes and for the way we should solve them.

http://www.institutnicod.org/seminaires-colloques/seminaires/doc-in-nicod-844/article/presentation-1400?lang=fr